CHICAGO — The detached dad, turning up his nose at diapering and too busy to bathe, dress and play with his kids, is mostly a myth, a government survey suggests. Most American fathers say they are heavily involved in hands-on parenting, the researchers found.

The nationally representative survey shows fathers’ involvement has increased slightly since the government first asked in 2002, coinciding with research since then that bolsters the benefits of hands-on fathering.

The results are encouraging and important “because others have found the more involved dads are, the better the outcomes for their children,” said researcher Jo Jones of the National Center for Health Statistics. She co-authored the report released Friday.

More academic success, fewer behavior problems and healthier eating habits are just some of the ways fathers’ involvement has been linked with children’s well-being.

“Times have changed,” said Robert Loftus, 34, of Yonkers. He quit a six-figure sales job a year ago to care for his two young children while his wife works full-time.

“We’re trying to rethink our priorities, and family seems to be the No. 1 priority whereas in the past maybe people were more focused on career,” he said.